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Derive an identity for nCk via inclusion-exclusion by counting the k-multisets of [n] in which each element of [n] appears at most once. use p_i = "element i appears more than once in the multiset" as the i-th property, for 1<=i<=n
what would be the force required to push a 100 pound object along a ramp that is inclined 10 degree with the horizonal.
Consider a standard deck of playing cards. You randomly select a card from the deck and find that you have drawn a face card.
Given a set of all real numbers containing 4s and 5s in their decimal representation. Determine the given set is countable or uncountable.
Five ounces of shrimp and 3 ounces of scallops contain 45 milligrams of cholesterol less than the suggested maximum daily intake. Determine the cholesterol content in an ounce of each item.
A motorcycle dealership has allocated 90% of its employees to the sales of motorcycles of which 70% of this 90% are male employees, this company has also determined that 80% of all its employees are male.
The consumer price index for a new car in 1990 was 110.2, and in 1995 it was 136.5. If the price of the car was $12,880 in 1990, what was the price in 1995?
Let I be an ideal of R and let S be a subring of R. prove that I(intersection)S is an ideal of S. ALSO, show by some example that not every ideal of a subring S of a ring R
Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli,shrimp, mushrooms, zucchini, green pepper}.
A set of data whose histogram is bell shaped yields a sample mean and standard deviation of 50 and 4, respectively. Approximately what proportion of observations are.
The measures of the angles of a triangle are in the ratio of 2:3:4. What is the measure of the smallest angle? Each side of a rhombus measures 10 inches. If one diagonal of the rhombus is 12 inches long, what is the length of the other diagonal?
Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section? Please show work.
Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.
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